where \(\mathcal {D}(A)\)  is a \((c \times c-1)\)  matrix of functions of \(A\) ; the
ML estimator[1]} takes
\(\mathcal {D}(A) = D^T(A; \alpha ,\beta ) V^{-1}(A; \alpha ,\beta )\) , where
\(D(A; \alpha ,\beta )\)  is the \((c-1 \times c)\)  gradient matrix of the
vector
\(\lbrace  I(Y \le 1) -\mbox{expit}(\alpha _1 + \beta A) ,\ldots , I(Y \le c-1)-\mbox{expit}(\alpha _{c-1} + \beta A)\rbrace ^T\)  in (REF ) with
respect to \(\alpha _1,\ldots ,\alpha _{c-1},\beta \) , and
\(V(A; \alpha ,\beta )\)  is its \((c-1 \times c-1)\)  conditional covariance
matrix given \(A\) .
